Modular Transport and Spherical Holographic Entanglement Entropy in a Source–Readout Architecture

This paper reconstructs the Casini–Huerta–Myers derivation of spherical entanglement entropy within Shadow Theory’s source–readout architecture. A single conformal vacuum supplies both the state restricted to a ball’s causal diamond and its thermal description on the hyperbolic cylinder. The paper derives the temperature normalization directly from modular flow at the level of observable algebras, without requiring a continuum density matrix. Under the classical holographic dictionary, the bulk construction recovers the same temperature and the regulated horizon entropy. The paper distinguishes the localization of observables from the regulator used to count states. It gives an exact criterion for when analytic cutoff changes preserve the finite entropy term in odd spacetime dimensions and shows that the logarithmic coefficient in even spacetime dimensions is invariant within the stated class. This explains how two cutoff prescriptions can agree at leading order and still give different finite entropy terms.